
This is the historic case studied by Cartan ([1]}, [2]}) and Engel ([3]}, [4]}).
There are local coordinates \((a_1,a_2,a_3,a_4,a_5)\)  (see pages 159–160 of [2]}) such that
\(\theta _1&={\rm d}a_1+\left(a_3+\frac{1}{2}a_4 a_5\right){\rm d}a_4,\\\theta _2&={\rm d}a_2+\left(a_3-\frac{1}{2}a_4 a_5\right){\rm d}a_5,\\\theta _3&={\rm d}a_3+\frac{1}{2}a_4 {\rm d}a_5-\frac{1}{2}a_5 {\rm d}a_4,\\\theta _4&={\rm d}a_4,\nonumber \\\theta _5&={\rm d}a_5.\nonumber \) 
